The 64-year-old man was crossing the road at the junction of Marchmont Road and Warrander Park Road when he was struck by a black cab.
He suffered severe head injuries, and died after being taken to Edinburgh Royal Infirmary.
The incident happened at about 03:10. Police have appealed for any witnesses to contact them.
A spokesman for the Lothian and Borders force said: “We are still trying to establish the full circumstances of this collision, which, tragically, resulted in a man’s death.
“Despite the time at which the incident occurred, there may have been other pedestrians or motorists in the area returning home who can perhaps help with our investigation.
“Anyone with information relevant to this enquiry is asked to contact police immediately.”
The road was closed for about four hours while officers carried out an investigation at the scene.